IDEAS home Printed from https://ideas.repec.org/a/bpj/jossai/v6y2018i2p165-177n5.html
   My bibliography  Save this article

Moving Average Model with an Alternative GARCH-Type Error

Author

Listed:
  • Zhu Huafeng

    (School of Economics and Statistics, Guangzhou University, Guangzhou510006, China)

  • Zhang Xingfa

    (School of Economics and Statistics, Guangzhou University, Guangzhou510006, China)

  • Liang Xin

    (School of Economics and Statistics, Guangzhou University, Guangzhou510006, China)

  • Li Yuan

    (School of Economics and Statistics, Guangzhou University, Guangzhou510006, China)

Abstract

Motivated by the double autoregressive model with order p (DAR(p) model), in this paper, we study the moving average model with an alternative GARCH error. The model is an extension from DAR(p) model by letting the order p goes to infinity. The quasi maximum likelihood estimator of the parameters in the model is shown to be asymptotically normal, without any strong moment conditions. Simulation results confirm that our estimators perform well. We also apply our model to study a real data set and it has better fitting performance compared to DAR model for the considered data.

Suggested Citation

  • Zhu Huafeng & Zhang Xingfa & Liang Xin & Li Yuan, 2018. "Moving Average Model with an Alternative GARCH-Type Error," Journal of Systems Science and Information, De Gruyter, vol. 6(2), pages 165-177, April.
    • Handle: RePEc:bpj:jossai:v:6:y:2018:i:2:p:165-177:n:5
    DOI: 10.21078/JSSI-2018-165-13
    as

    Download full text from publisher

    File URL: https://doi.org/10.21078/JSSI-2018-165-13
    Download Restriction: no
    File URL: https://libkey.io/10.21078/JSSI-2018-165-13?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Min Chen & Dong Li & Shiqing Ling, 2014. "Non-Stationarity And Quasi-Maximum Likelihood Estimation On A Double Autoregressive Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(3), pages 189-202, May.
    2. Christensen, Bent Jesper & Dahl, Christian M. & Iglesias, Emma M., 2012. "Semiparametric inference in a GARCH-in-mean model," Journal of Econometrics, Elsevier, vol. 167(2), pages 458-472.
    3. Shiqing Ling & Dong Li, 2008. "Asymptotic inference for a nonstationary double AR (1) model," Biometrika, Biometrika Trust, vol. 95(1), pages 257-263.
    4. Li, Dong & Ling, Shiqing & Zakoïan, Jean-Michel, 2015. "Asymptotic inference in multiple-threshold double autoregressive models," Journal of Econometrics, Elsevier, vol. 189(2), pages 415-427.
    5. Xingfa Zhang & Heung Wong & Yuan Li, 2016. "A functional coefficient GARCH-M model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(13), pages 3807-3821, July.
    6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    7. Yuzhi Cai & Gabriel Montes‐Rojas & Jose Olmo, 2013. "Quantile Double AR Time Series Models for Financial Returns," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(6), pages 551-560, September.
    8. Shiqing Ling, 2004. "Estimation and testing stationarity for double‐autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 63-78, February.
    9. Liu, Ji-Chun, 2012. "Structure of a double autoregressive process driven by a hidden Markov chain," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1468-1473.
    10. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Guo, Shaojun & Li, Dong & Li, Muyi, 2019. "Strict stationarity testing and GLAD estimation of double autoregressive models," Journal of Econometrics, Elsevier, vol. 211(2), pages 319-337.
    2. Zhu, Huafeng & Zhang, Xingfa & Liang, Xin & Li, Yuan, 2017. "On a vector double autoregressive model," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 86-95.
    3. Li, Dong & Tao, Yuxin & Yang, Yaxing & Zhang, Rongmao, 2023. "Maximum likelihood estimation for α-stable double autoregressive models," Journal of Econometrics, Elsevier, vol. 236(1).
    4. Huan Gong & Dong Li, 2020. "On the three‐step non‐Gaussian quasi‐maximum likelihood estimation of heavy‐tailed double autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 883-891, November.
    5. Aknouche, Abdelhakim, 2015. "Unified quasi-maximum likelihood estimation theory for stable and unstable Markov bilinear processes," MPRA Paper 69572, University Library of Munich, Germany.
    6. Zhu, Qianqian & Zheng, Yao & Li, Guodong, 2018. "Linear double autoregression," Journal of Econometrics, Elsevier, vol. 207(1), pages 162-174.
    7. Min Chen & Dong Li & Shiqing Ling, 2014. "Non-Stationarity And Quasi-Maximum Likelihood Estimation On A Double Autoregressive Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(3), pages 189-202, May.
    8. Guodong Li & Qianqian Zhu & Zhao Liu & Wai Keung Li, 2017. "On Mixture Double Autoregressive Time Series Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 306-317, April.
    9. Dong Li & Shiqing Ling & Rongmao Zhang, 2016. "On a Threshold Double Autoregressive Model," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(1), pages 68-80, January.
    10. Kai Yang & Qingqing Zhang & Xinyang Yu & Xiaogang Dong, 2023. "Bayesian inference for a mixture double autoregressive model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(2), pages 188-207, May.
    11. Francq, Christian & Zakoian, Jean-Michel, 2013. "Inference in non stationary asymmetric garch models," MPRA Paper 44901, University Library of Munich, Germany.
    12. Christian M. Dahl & Emma M. Iglesias, 2008. "The limiting properties of the QMLE in a general class of asymmetric volatility models," CREATES Research Papers 2008-38, Department of Economics and Business Economics, Aarhus University.
    13. Djogbenou, Antoine & Inan, Emre & Jasiak, Joann, 2023. "Time-varying coefficient DAR model and stability measures for stablecoin prices: An application to Tether," Journal of International Money and Finance, Elsevier, vol. 139(C).
    14. Wang, Gaowen, 2006. "A note on unit root tests with heavy-tailed GARCH errors," Statistics & Probability Letters, Elsevier, vol. 76(10), pages 1075-1079, May.
    15. Iglesias, Emma M., 2015. "Value at Risk and expected shortfall of firms in the main European Union stock market indexes: A detailed analysis by economic sectors and geographical situation," Economic Modelling, Elsevier, vol. 50(C), pages 1-8.
    16. Anthony J. Lawrance, 2010. "Volatile ARMA Modelling of GARCH Squares," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 2(3), pages 195-203, June.
    17. Iglesias Emma M, 2009. "Finite Sample Theory of QMLEs in ARCH Models with an Exogenous Variable in the Conditional Variance Equation," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(2), pages 1-30, May.
    18. Meister, Alexander & Kreiß, Jens-Peter, 2016. "Statistical inference for nonparametric GARCH models," Stochastic Processes and their Applications, Elsevier, vol. 126(10), pages 3009-3040.
    19. Francq, Christian & Zakoïan, Jean-Michel, 2015. "Risk-parameter estimation in volatility models," Journal of Econometrics, Elsevier, vol. 184(1), pages 158-173.
    20. Karapanagiotidis, Paul, 2013. "Empirical evidence for nonlinearity and irreversibility of commodity futures prices," MPRA Paper 56801, University Library of Munich, Germany.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:jossai:v:6:y:2018:i:2:p:165-177:n:5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.